Brightness varies between texture image and UV or edit mode
It looks like you completely baked your textures before you set up any (or enough) lighting. Therefore the texture (in its normal form, as seen in your red "texture image" box) was evaluated in the dimly lit scene you use. Then you used that as the material texture, which is also why the same darker texture is visible in the "textured view". To solve this you could bake again but after setting up some lighting or just bake with different settings for example only bake "textures" (without shading) Make sure you only bake "textures" https://docs.blender.org/manual/en/latest/render/blender_render/bake.html

If this doesn't solve your problem maybe look for a wrong node in your material setup or provide your .blend file, since there might be other problems with the same symptoms.

Happy Blending! :)